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I'd rather check all the answers quickly by comparing each fraction to it's reciprocal

A 8/10 = 10/8 which is 64=100 (36% smaller) B 11/10 = 10/11 which is 121=100 (21% larger) C 15/10 = 10/15 which is 225=100 (125% larger) D 18/10 = 10/18 which is 324=100 <- correct 324 is 224% larger than 100 E 22/10 = 10/22 which is 484=100 (384% larger)

this shouldn't take more than 1:00 if you are comfortable with squares of numbers >10 Cheers M

You should see the difference between 'a is N% bigger than b' and 'a is N% of b'. In the first case a - b = N%b, while in the second a = N%b. That's why a^2=3.24, but not 2.24.

I m just confused with the wording, not the logic.

Do we always consider this 224% to be calculate for the number we comparing. My doubt is there coz of this statement 224% greater than y..no where stated 224% of x or y.

X is 224% bigger then its reciprocal X = (224/100 + 1 ) * 1/X X^2=3.24 Now just solve for X ******** Tricks for faster way to solve the equation: (224/100 +1) = 3.24 and there is only 3 answer choices that can produce 4 in last digit when you square it. .8^2 doesn't come close to 3.24 and 2.2^2 is easy to guess not to be 324. That leaves only one choice left, 1.8!!!

I wasn't sure how to answer this at first, so I decided to try and estimate what numbers were close to twice the reciprocals. "A" was an obvious elimination since the reciprical increased instead of decreased and "E" was too big. I ended up going with "C", which is a trap answer if you forget to add 1 to 224%.

It is a good idea to know the squares of integers between 1 and 20. Not compulsory to know, but still helpful if one does.

Another method (back-solving):

Alternatively, we could test the given options, find out which options is 3.24 times its reciprocal. It is also helpful to know the reciprocals of the first dozen positive integers, i.e. 1/1;1/2;1/3....1/12. Again, you don't have to know this, but it can help you convert into decimals easily. Let us test the option. A) 0.8 aka 4/5, whose reciprocal is 5/4 aka 1.25. ELIMINATE because the reciprocal is actually greater than the number, but we want the reciprocal to be (approximately) a third (or 1/3.24) of the number. B) 1.1 aka 11/10, whose reciprocal is 10/11 aka is 0.909. ELIMINATE because the reciprocal is not approx a third of the number. C) 1.5 aka 3/2, whose reciprocal is 2/3 aka 0.666. ELIMINATE because the reciprocal is not approx a third of the number. D) 1.8 aka 18/10 aka 9/5, whose reciprocal is 5/9 aka 0.555. KEEP because the reciprocal is approx a third of the number. CORRECT ANSWER. E) 2.2 aka 11/5, whose reciprocal is 5/11 aka 0.4545. ELIMINATE because the reciprocal is not approx a third of the number.

Both solutions yield D as the answer.

Personally, I find the method testing numbers easier faster to use, IN GENERAL, but for this particular question, algebra was far quicker. The testmakers design the questions with a specific "easier" solution in mind. It is important for the student to be flexible in order to use the "better" method to solve a PARTICULAR question. Hope you find this useful.